Main Article Content
Abstract
Purpose: Transportation problem plays an important role in operations research. The more generalized cases of transportation problems are trans-shipment problems. Further, the trans-shipment problems may have a set of trans-shipment nodes, or the source/destination nodes themselves act as the trans-shipment nodes. The study of the trans-shipment problems and their solution methodology is the goal of this paper.
Methodology: The solution of a trans-shipment problem could be done by transferring it to a transportation problem. Further, there exist various conventional methods for solving the transportation problem. The present paper discusses about the scope of application of an existing heuristic algorithm directly over the trans-shipment problem. The heuristic is based on the minimum spanning tree approach. We implement the algorithm over a test problem and further compare its performance by the performance of the corresponding algorithm Vogel’s Approximation Method.
Main findings: The spanning tree approach gives a better solution or almost the nearby solution as compared to the solution obtained by Vogel’s Approximation Method.
Implications: The solution obtained by the spanning-tree approach takes lesser computational effort to reach a better feasible solution.
The novelty of study: The algorithm to deal with the trans-shipment problem i.e. for finding the feasible solution of the trans-shipment problem is the main focus of this paper.Transportation Problem
Keywords
Article Details
Authors retain the copyright without restrictions for their published content in this journal. IJSRTM is a SHERPA ROMEO Journal.
Publishing License
This is an open-access article distributed under the terms of 
References
- Agadaga, G. O. & Akpan, N. P. (2017). Trans-shipment Problem and Its Variants: A Review. Mathematical Theory and Modeling, 7(2), pp.19-32.
- Akpan, N. P. & Iwok, I. A. (2017). A minimum spanning tree approach of solving a transportation problem. International Journal of Mathematics and Statistics Invention, 5(3), pp.09-18.
- Aljanabi, K. B. & Jasim, A. N. (2015). An Approach for Solving Transportation Problem Using Modified Kruskal’s Algorithm. International Journal of Science and Research (IJSR), 4(7), pp.2426-2429.
- AntoÅ¡, K. (2016). The Use of Minimal Spanning Tree for Optimizing Ship Transportation. NAÅ E MORE: znanstveno-struÄniÄasopisza more i pomorstvo, 63(3 Special Issue), pp.81-85. https://doi.org/10.17818/NM/2016/SI1 DOI: https://doi.org/10.17818/NM/2016/SI1
- Dubey, O. P., Deep, K. & Nagar, A. (2014). Goal Programming Approach To Trans-Shipment Problem, B. V. Babu et.al. (Eds.): Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS-2012), Advances in Intelligent and Soft Computing (AISC), Springer, India, ISSN 2194-5357, Vol. 236, Page: 337-343. https://doi.org/10.1007/978-81-322-1602-5_37 DOI: https://doi.org/10.1007/978-81-322-1602-5_37
- Gen, M., Li, Y. & Ida, K. (1999). Solving multi-objective transportation problem by spanning tree-based genetic algorithm. IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences, 82(12), pp.2802-2810.
- Greenberg, H. J. (1998). Greedy algorithms for minimum spanning tree. University of Colorado at Denver.
- Jo, J. B., Li, Y. & Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering, 53(2), pp.290-298. https://doi.org/10.1016/j.cie.2007.06.022 DOI: https://doi.org/10.1016/j.cie.2007.06.022
- Kruskal, J. B., (1956). On the shortest spanning sub-tree of a graph and the travelling salesman problem. Proceedings of the American Mathematical society, 7(1), pp.48-50. https://doi.org/10.1090/S0002-9939-1956-0078686-7 DOI: https://doi.org/10.1090/S0002-9939-1956-0078686-7
- Molla, A. Z. S., Sanei, M., Soltani, R. & Mahmoodirad, A. (2014). Solving a step fixed charge transportation problem by a spanning tree-based memetic algorithm.
References
Agadaga, G. O. & Akpan, N. P. (2017). Trans-shipment Problem and Its Variants: A Review. Mathematical Theory and Modeling, 7(2), pp.19-32.
Akpan, N. P. & Iwok, I. A. (2017). A minimum spanning tree approach of solving a transportation problem. International Journal of Mathematics and Statistics Invention, 5(3), pp.09-18.
Aljanabi, K. B. & Jasim, A. N. (2015). An Approach for Solving Transportation Problem Using Modified Kruskal’s Algorithm. International Journal of Science and Research (IJSR), 4(7), pp.2426-2429.
AntoÅ¡, K. (2016). The Use of Minimal Spanning Tree for Optimizing Ship Transportation. NAÅ E MORE: znanstveno-struÄniÄasopisza more i pomorstvo, 63(3 Special Issue), pp.81-85. https://doi.org/10.17818/NM/2016/SI1 DOI: https://doi.org/10.17818/NM/2016/SI1
Dubey, O. P., Deep, K. & Nagar, A. (2014). Goal Programming Approach To Trans-Shipment Problem, B. V. Babu et.al. (Eds.): Proceedings of the Second International Conference on Soft Computing for Problem Solving (SocProS-2012), Advances in Intelligent and Soft Computing (AISC), Springer, India, ISSN 2194-5357, Vol. 236, Page: 337-343. https://doi.org/10.1007/978-81-322-1602-5_37 DOI: https://doi.org/10.1007/978-81-322-1602-5_37
Gen, M., Li, Y. & Ida, K. (1999). Solving multi-objective transportation problem by spanning tree-based genetic algorithm. IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences, 82(12), pp.2802-2810.
Greenberg, H. J. (1998). Greedy algorithms for minimum spanning tree. University of Colorado at Denver.
Jo, J. B., Li, Y. & Gen, M. (2007). Nonlinear fixed charge transportation problem by spanning tree-based genetic algorithm. Computers & Industrial Engineering, 53(2), pp.290-298. https://doi.org/10.1016/j.cie.2007.06.022 DOI: https://doi.org/10.1016/j.cie.2007.06.022
Kruskal, J. B., (1956). On the shortest spanning sub-tree of a graph and the travelling salesman problem. Proceedings of the American Mathematical society, 7(1), pp.48-50. https://doi.org/10.1090/S0002-9939-1956-0078686-7 DOI: https://doi.org/10.1090/S0002-9939-1956-0078686-7
Molla, A. Z. S., Sanei, M., Soltani, R. & Mahmoodirad, A. (2014). Solving a step fixed charge transportation problem by a spanning tree-based memetic algorithm.